
SPLIT DUAL JACOBSTHAL AND JACOBSTHAL-LUCAS QUATERNIONS
Asian Journal of Mathematics and Computer Research,
Page 1-9
DOI:
10.56557/ajomcor/2022/v29i37938
Abstract
Many researchs have been studied on quaternions since Hamilton introduced them to the literature in 1843. In our paper, we gave split dual Jacobsthal (SDJ) and split dual Jacobsthal-Lucas (SDJL) quaternions over the algebra H(μ,n) with the basis {1; e1; e2; e3}, where μ,n ∈ Z. Binet like formulaes are obtained for these quaternions. Also, given Vajda identities for SDJ and SDJL quaternions.As a special case of Vajda identities, d'Ocagne's, Cassini's and Catalan's identities are represented.
Keywords:
- quaternions
- dual Jacobsthal and dual Jacobsthal-Lucas numbers
- plit dual Jacobsthal and split dual Jacobsthal-Lucas quaternions
How to Cite
TOKESER, U., & UNAL, Z. (2022). SPLIT DUAL JACOBSTHAL AND JACOBSTHAL-LUCAS QUATERNIONS. Asian Journal of Mathematics and Computer Research, 29(3), 1-9. https://doi.org/10.56557/ajomcor/2022/v29i37938
References
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Yagmur T. Split Jacobsthal and Jacobsthal-Lucas Quaternions. Communications in Mathematics and Applications. 2019; 10(3):429-438.
Horadam AF. Complex Fibonacci numbers and Fibonacci Quaternions. Am. Math. Monthly. 1963; 70(3):289-291.
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Halc S. On Fibonacci Quaternions. Adv. Appl. Cliord Algebras. 2012; 22(2):321-327.
Tokeser U, Unal Z, Bilgici G. Split Pell and Pell-Lucas Quaternions. Adv. Appl. Cliord Algebras. 2017; 27(2):1881-1893.
Akyigit M, Kosal HH, Tosun M. Split Fibonacci Quaternions. Adv. Appl. Cliord Algebras. 2013; 23(3):535-545.
Horadam AF. Jacobsthal Representation Numbers. The Fibonacci Quart. 1996; 34:40-54.
Ercan Z, Yuce S. On Properties of The Dual Quaternions. European Journal of Pure and Applied Math. 2011; 4(2):142-146.
Szynal-Liana A, Wloch I. A Note on Jacobsthal Quaternions. Adv. Appl. Cliord Algebras. 2016; 26(1):441-447.
Horadam AF. Jacobsthal Representation Polynomials. The Fibonacci Quart. 1997; 35:137-148.
Horadam AF. Jacobsthal and Pell Curves. The Fibonacci Quart. 1988; 26:79-83.
Aydin FT, Yuce S. A New Approach to Jacobsthal Quaternions. Filomat. 2017; 31(8):5567-
Cerin Z. Formulae for Sums of Jacobsthal-Lucas Numbers. International Mathematical Forum. 2007; 2(40):1969-1984.
Cerin Z. Sums of Squares and Products of Jacobsthal Numbers. Journal of Integer Sequence. 2007; Article 07.2.5.
Cerin Z. Some Alternating Sums of Lucas Numbers. Central European J. Math. 2005; 3:1-13.
Djordjevic GB. Generalized Jacobsthal Polynomials. The Fibonacci Quart. 2009; 38:239-243.
Yagmur T. Split Jacobsthal and Jacobsthal-Lucas Quaternions. Communications in Mathematics and Applications. 2019; 10(3):429-438.
Horadam AF. Complex Fibonacci numbers and Fibonacci Quaternions. Am. Math. Monthly. 1963; 70(3):289-291.
Cliord WK. Preliminary Sketch of bi-Quaternions. Proc. Lond. Math. Soc. 1871; 4:381-395.
Swamy MN. On Generalized Fibonacci Quaternions. The Fibonacci Quart. 1973; 11(5):547-
Halc S. On Fibonacci Quaternions. Adv. Appl. Cliord Algebras. 2012; 22(2):321-327.
Tokeser U, Unal Z, Bilgici G. Split Pell and Pell-Lucas Quaternions. Adv. Appl. Cliord Algebras. 2017; 27(2):1881-1893.
Akyigit M, Kosal HH, Tosun M. Split Fibonacci Quaternions. Adv. Appl. Cliord Algebras. 2013; 23(3):535-545.
Horadam AF. Jacobsthal Representation Numbers. The Fibonacci Quart. 1996; 34:40-54.
Ercan Z, Yuce S. On Properties of The Dual Quaternions. European Journal of Pure and Applied Math. 2011; 4(2):142-146.
Szynal-Liana A, Wloch I. A Note on Jacobsthal Quaternions. Adv. Appl. Cliord Algebras. 2016; 26(1):441-447.
Horadam AF. Jacobsthal Representation Polynomials. The Fibonacci Quart. 1997; 35:137-148.
Horadam AF. Jacobsthal and Pell Curves. The Fibonacci Quart. 1988; 26:79-83.
Aydin FT, Yuce S. A New Approach to Jacobsthal Quaternions. Filomat. 2017; 31(8):5567-
Cerin Z. Formulae for Sums of Jacobsthal-Lucas Numbers. International Mathematical Forum. 2007; 2(40):1969-1984.
Cerin Z. Sums of Squares and Products of Jacobsthal Numbers. Journal of Integer Sequence. 2007; Article 07.2.5.
Cerin Z. Some Alternating Sums of Lucas Numbers. Central European J. Math. 2005; 3:1-13.
Djordjevic GB. Generalized Jacobsthal Polynomials. The Fibonacci Quart. 2009; 38:239-243.
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